Approximations

Question 1

What are the reasons for approximations?

Answer 1

Save storage for a computing
Model the value in simple manner
The tools available cannot use the full accuracy of the value
It is necessary to round to a finite decimal place such as currency

Question 2

What is the error?

Answer 2

The error of an approximation is the difference between the exact value and approximation

Question 3

What is the formula for finding the error?

Answer 3

Error = X - x

Where the exact value is ‘x’ and approximation is ‘X’

Question 4

What is the absolute error?

Answer 4

The absolute error is defined as the absolute value of the error. The absolute error is to find the modulus; it is always positive

Question 5

What is the equation for the absolute error?

Answer 5

Absolute error = I X-x I

Question 6

What is the relative error?

Answer 6

Relative error is the ratio of the error to the exact value

Question 7

What is the equation for the relative error?

Answer 7

X-x/x if x != 0

Where exact value is ‘x’ and the approximation is ‘X’

Question 8

What is absolute relative error?

Answer 8

Absolute relative error is the ratio of the size of the error to the magnitude of the exact value

Question 9

What is the equation of absolute relative error?

Answer 9

Absolute relative error = I X-x/x I

Question 10

What is percentage error?

Answer 10

When the absolute relative error is expressed as a percentage, it is called percentage error

Question 11

What is the equation of which radian-degree conversion is derived?

Answer 11

180^o = (pi)(radians)

Question 12

How do you convert from degrees to radians?

Answer 12

Degrees* (pi/180) = Radians

Question 13

How to convert from radians to degrees?

Answer 13

Radians * 180/pi = Degrees

Question 14

What are the rules for answering questions with pi and radians?

Answer 14

If an angle is simple and is to be given as radians, leave the answer in pi form
All measurements in pi are assumed to be in radians

Question 15

What is the equation for maximum error of a number rounded to ‘n’ decimal places?

Answer 15

5*10^-n-1

Question 16

What is chopping?

Answer 16

Chopping is where the numbers after a specified number of decimal places are omitted

Question 17

What is the equation for the maximum possible error when a number is chopped to ‘n’ decimal places?

Answer 17

Error < 1 x 10^-n

Question 18

What is the average error in each value of a rounded value?

Answer 18

The average error in each value is 0 as the error of numbers rounded up and rounded down cancel each other

Question 19

What is the average error of a chopped value?

Answer 19

This is the maximum error divided by 2. This is because numbers cannot be rounded down so the lowest error is 0.

Question 20

What is the formula for expected error of a data set?

Answer 20

Number of values in data set * Average error

Question 21

What is the error interval?

Answer 21

The error interval are the limits of accuracy when a number has been rounded or truncated

Question 22

What answer do you give when a question asks for interval estimate?

Answer 22

Using the estimate, calculate the answer of which both bounds round to
If this is not possible, the question is a precautionary example

Question 23

What is the approximation for the relative error of XY?

Answer 23

R₁ + R₂

Where R₁ is the relative error of X/x and R₂ is the relative error of Y/y

Question 24

How does the approximation of relative error differ from the approximation of absolute relative error?

Answer 24

Rather than R₁ +- R₂, the approximation for absolute relative error for X and Y is IR₁ +- R₂I

Question 25

What is an ill-conditioned problem?

Answer 25

A problem is called ill-conditioned if a small relative error in data can cause a large relative error in the computed solution regardless of the method